Classification of pseudo-reductive groups /
Brian Conrad, Gopal Prasad.
- 1 online resource (1 volume)
- Annals of mathematics studies ; number 191 .
- Annals of mathematics studies ; no. 191. .
Includes bibliographical references and index.
Cover; Title; Copyright; Contents; 1 Introduction; 1.1 Motivation; 1.2 Root systems and new results; 1.3 Exotic groups and degenerate quadratic forms; 1.4 Tame central extensions; 1.5 Generalized standard groups; 1.6 Minimal type and general structure theorem; 1.7 Galois-twisted forms and Tits classification; 1.8 Background, notation, and acknowledgments; 2 Preliminary notions; 2.1 Standard groups, Levi subgroups, and root systems; 2.2 The basic exotic construction; 2.3 Minimal type; 3 Field-theoretic and linear-algebraic invariants; 3.1 A non-standard rank-1 construction
In the earlier monograph Pseudo-reductive Groups, Brian Conrad, Ofer Gabber, and Gopal Prasad explored the general structure of pseudo-reductive groups. In this new book, Classification of Pseudo-reductive Groups, Conrad and Prasad go further to study the classification over an arbitrary field. An isomorphism theorem proved here determines the automorphism schemes of these groups. The book also gives a Tits-Witt type classification of isotropic groups and displays a cohomological obstruction to the existence of pseudo-split forms. Constructions based on regular degenerate quadratic forms and new techniques with central extensions provide insight into new phenomena in characteristic 2, which also leads to simplifications of the earlier work. A generalized standard construction is shown to account for all possibilities up to mild central extensions. The results and methods developed in Classification of Pseudo-reductive Groups will interest mathematicians and graduate students who work with algebraic groups in number theory and algebraic geometry in positive characteristic.
In English.
1400874025 9781400874026
10.1515/9781400874026 doi
832712 MIL 22573/ctt193f7hw JSTOR 9452403 IEEE
2015023803
Linear algebraic groups. Group theory. Geometry, Algebraic. Groupes lin�eaires alg�ebriques. Th�eorie des groupes. G�eom�etrie alg�ebrique. MATHEMATICS--Algebra--Intermediate. MATHEMATICS--Mathematical Analysis. Geometry, Algebraic. Group theory. Linear algebraic groups.